多量测向量模型下基于贝叶斯检验的快速OMP算法研究

doi:10.11999/JEIT151131

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摘要

目前多量测向量(Multiple Measurement Vectors, MMV)模型的稀疏重构算法存在两个问题：计算复杂度高和当重构的支撑集存在冗余时无法有效剔除。为同时提高MMV模型的重构效率和重构精度，该文提出一种MMV模型下基于贝叶斯检验的快速正交匹配追踪(Fast Orthogonal Matching Pursuit based on Bayesian Testing, FOMP-BT)算法。首先，通过新原子组选和warm start求逆的思想来减少算法总的迭代次数以及每次迭代的运算量，以提高算法的重构效率；其次，利用贝叶斯检验的思想剔除冗余支撑集以提高重构精度；最后对所研究的算法从参数选择以及计算复杂度等方面进行了理论分析。仿真结果表明，所提算法具有重构精度高、速度快以及对噪声有较好的鲁棒性等优势。

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	李少东
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	马晓岩

关键词 ：多量测向量模型, 快速正交匹配追踪算法, 迭代次数, 贝叶斯检验

Abstract：

There are two issues in the Sparse Reconstruction (SR) algorithm of Multiple Measurement Vectors (MMV). One is the high computation complexity and the other is that redundant support set can not be effectively removed. In order to improve the efficiency and accuracy of SR algorithm simultaneously for MMV model, a Fast Orthogonal Matching Pursuit algorithm based on Bayesian Test (FOMP-BT) is presented in this paper. Firstly, the total number of iterations and the computation of each iteration are reduced through the new atomic group selection and warm start matrix inversion, thus the efficiency of the algorithm is improved. Secondly, using the idea of the Bayesian test to eliminate redundant support set, the accuracy of reconstruction is improved. Finally, the theoretical analysis of the algorithm is carried out from the aspects of parameter selection and computation complexity. The simulation results show that the proposed algorithm has the advantages of high accuracy, fast speed and good robustness to noise.

Key words： Multiple measurement vectors model Fast Orthogonal Matching Pursuit (FOMP) algorithm Number of iterations Bayesian test

收稿日期: 2015-10-10 出版日期: 2016-04-07

PACS:

TN957.52

通讯作者: 李少东：男，1987年生，博士，研究方向为压缩感知理论在雷达成像中的应用. E-mail: liying198798@126.com

作者简介: 李少东：男，1987年生，博士，研究方向为压缩感知理论在雷达成像中的应用. 陈文峰：男，1989年生，博士，研究方向为雷达目标检测与识别. 杨军：男，1973年生，副教授，硕士生导师，研究方向为雷达目标检测、现代信号处理. 马晓岩：男，1962年生，教授，博士生导师，研究方向为雷达目标检测与识别.

引用本文:

李少东,陈文峰,杨军,马晓岩. 多量测向量模型下基于贝叶斯检验的快速OMP算法研究[J]. 电子与信息学报, 2016, 38(7): 1731-1737. LI Shaodong, CHEN Wenfeng, YANG Jun, MA Xiaoyan. Fast OMP Algorithm Based on Bayesian Test for Multiple Measurement Vectors Model. JEIT, 2016, 38(7): 1731-1737.

链接本文:

http://jeit.ie.ac.cn/CN/10.11999/JEIT151131 或 http://jeit.ie.ac.cn/CN/Y2016/V38/I7/1731

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